Agent-based Financial Markets and Volatility Dynamics
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Agent-based Financial Markets and Volatility Dynamics Blake LeBaron International Business School Brandeis University www.brandeis.edu/ ~blebaron
description
Agent-based Financial Markets and Volatility Dynamics. Blake LeBaron International Business School Brandeis University www.brandeis.edu/~blebaron. Fundamental Input. Market Output. Price Volatility Volume d/p ratios Liquidity. Geometric Random Walk. Agent-based Financial Market. - PowerPoint PPT Presentation
Transcript of Agent-based Financial Markets and Volatility Dynamics
Agent-based Financial Markets and Volatility
Dynamics
Blake LeBaron
International Business School
Brandeis University
www.brandeis.edu/~blebaron
GeometricRandom Walk
PriceVolatilityVolumed/p ratiosLiquidity
Agent-basedFinancial Market
Fundamental Input Market Output
Overview
Agent-based financial marketsExample marketPrices and volatilityFuture challenges
Agent-based Financial Markets
Many interacting strategiesEmergent features
Correlations and coordination Macro dynamics
Bounded rationality
Bounded Rationality andSimple Rules
Why? Computational limitations Environmental complexity
Behavioral arguments Psychological biases Simple, robust heuristics
Computationally tractable strategies
Agent-based Economic Models
Website:Leigh Tesfatsion at Iowa St.http://www.econ.iastate.edu/tesfatsi/ace.htm
Handbook of Computational Economics (vol 2), Tesfatsion and Judd, forthcoming 2006.
Example Market
Detailed description: Calibrating an agent-based financial
market
Assets
Equity Risky dividend (Weekly)
Annual growth = 2%, std. = 6% Growth and variability in U.S. annual data Fixed supply (1 share)
Risk free Infinite supply Constant interest: 0% per year
Agents
500 Agents Intertemporal CRRA(log) utility
Consume constant fraction of wealth Myopic portfolio decisions
Trading Rules
250 rules (evolving) Information converted to portfolio
weights Fraction of wealth in risky asset [0,1]
Neural network structure Portfolio weight = f(info(t))
Information Variables
Past returnsTrend indicatorsDividend/price ratios
Rules as Dynamic Strategies
Time
0
1
Portfolio weight
f(info(t))
Portfolio Decision
Maximize expected log portfolio returnsEstimate over memory length histories
Olsen et al. Levy, Levy, Solomon(1994,2000)
Restrictions No borrowing No short sales
Heterogeneous Memories(Long versus Short Memory)
Return History
2 years
5 years
6 months
Past Future
Present
Short Memory: Psychology and Econometrics
Gambler’s fallacy/Law of small numbers Is this really irrational?
Regime changes Parameter changes Model misspecification
Agent Wealth Dynamics
MemoryShort Long
New Rules: Genetic Algorithm
Parent set = rules in useModify neural network weightsOperators:
Mutation Crossover Initialize
GA Replaces Unused Rules
In Use
Unused
Trading
Rules chosenDemand = f(p)Numerically clear marketTemporary equilibrium
Homogeneous Equilibrium
Agents hold 100 percent equityPrice is proportional to dividend
Price/dividend constantUseful benchmark
Two Experiments
All Memory Memory uniform 1/2-60 years
Long Memory Memory uniform 55-60 years
Time series sample Run for 50,000 weeks (~1000 years) Sample last 10,000 weeks (~200 years)
Financial Data
Weekly S&P (Schwert and Datastream) Period = 1947 - 2000 (Wednesday) Simple nominal returns (w/o dividends)
Weekly IBM returns and volume (Datastream)
Annual S&P (Shiller) Real S&P and dividends Short term interest
Price ComparisonAll Memory
Price ComparisonLong Memory
Price ComparisonReal S&P 500 (Shiller)
Weekly Returns
Weekly Return Histograms
Quantile RangesQ(1-x)-Q(x): Divided by Normal ranges
S&P weekly All memory
Q(0.95)-Q(0.05) 0.86 0.88
Q(0.99)-Q(0.01) 1.17 1.19
Price/return Features
MeanVarianceExcess kurtosis (Fat tails)Predictability (little)Long horizons (1 year)
Near Gaussian Slow convergence to fundamentals
Volatility Features
Persistence/long memoryVolatility/volumeVolatility asymmetry
Absolute Return Autocorrelations
Trading Volume Autocorrelations
Volume/Volatility Correlation
Returns /Absolute Returns
Crashes and Volume
Large price decreases and Trading volume Rule dispersion
Price and Trading Volume
Price and Rule Dispersion
Summary
Replicating many volatility features Persistence Volume connections Asymmetry
Crashes, homogeneity, and liquidity (price impact)
Simple behavioral foundations Not completely rational Well defined
Future Challenges
Model implementationValidationApplications
Model Implementation
ComplicatedCompute boundNonlinear features
Estimation Ergodicity
Future Validation Tools
Data inputs Price and dividend series training Wealth distributions
Agent calibration Micro data Experimental data
Live market information/interaction
Applications
Volatility/volume models Estimation and identification Risk prediction (crash probabilities)
Market and trader designPolicy
Interventions Systemic risk
Forecasting
